Chapter 18. Introduction to Modeling Multiphase · PDF fileIntroduction to Modeling Multiphase...

Chapter 18. Introduction to Modeling

Multiphase Flows

A large number of flows encountered in nature and technology are a mix-ture of phases. Physical phases of matter are gas, liquid, and solid, butthe concept of phase in a multiphase flow system is applied in a broadersense. In multiphase flow, a phase can be defined as an identifiable classof material that has a particular inertial response to and interaction withthe flow and the potential field in which it is immersed. For example,different-sized solid particles of the same material can be treated as dif-ferent phases because each collection of particles with the same size willhave a similar dynamical response to the flow field.

This chapter provides an overview of multiphase modeling in FLUENT,and Chapters 19 and 20 provide details about the multiphase modelsmentioned here. Chapter 21 provides information about melting andsolidification.

Information in this chapter is presented in the following sections:

• Section 18.1: Multiphase Flow Regimes

• Section 18.2: Examples of Multiphase Systems

• Section 18.3: Approaches to Multiphase Modeling

• Section 18.4: Choosing a Multiphase Model

c© Fluent Inc. November 28, 2001 18-1

Introduction to Modeling Multiphase Flows

18.1 Multiphase Flow Regimes

Multiphase flow can be classified by the following regimes, grouped intofour categories:

• gas-liquid or liquid-liquid flows

– bubbly flow: discrete gaseous or fluid bubbles in a continuousfluid

– droplet flow: discrete fluid droplets in a continuous gas

– slug flow: large bubbles in a continuous fluid

– stratified/free-surface flow: immiscible fluids separated by aclearly-defined interface

• gas-solid flows

– particle-laden flow: discrete solid particles in a continuous gas

– pneumatic transport: flow pattern depends on factors suchas solid loading, Reynolds numbers, and particle properties.Typical patterns are dune flow, slug flow, packed beds, andhomogeneous flow.

– fluidized beds: consist of a vertical cylinder containing parti-cles where gas is introduced through a distributor. The gasrising through the bed suspends the particles. Depending onthe gas flow rate, bubbles appear and rise through the bed,intensifying the mixing within the bed.

• liquid-solid flows

– slurry flow: transport of particles in liquids. The fundamentalbehavior of liquid-solid flows varies with the properties of thesolid particles relative to those of the liquid. In slurry flows,the Stokes number (see Equation 18.4-4) is normally less than1. When the Stokes number is larger than 1, the characteristicof the flow is liquid-solid fluidization.

– hydrotransport: densely-distributed solid particles in a con-tinuous liquid

18-2 c© Fluent Inc. November 28, 2001

18.2 Examples of Multiphase Systems

– sedimentation: a tall column initially containing a uniformdispersed mixture of particles. At the bottom, the particleswill slow down and form a sludge layer. At the top, a clearinterface will appear, and in the middle a constant settlingzone will exist.

• three-phase flows (combinations of the others listed above)

Each of these flow regimes is illustrated in Figure 18.1.1.

18.2 Examples of Multiphase Systems

Specific examples of each regime described in Section 18.1 are listedbelow:

• Bubbly flow examples: absorbers, aeration, air lift pumps, cavita-tion, evaporators, flotation, scrubbers

• Droplet flow examples: absorbers, atomizers, combustors, cryo-genic pumping, dryers, evaporation, gas cooling, scrubbers

• Slug flow examples: large bubble motion in pipes or tanks

• Stratified/free-surface flow examples: sloshing in offshore separatordevices, boiling and condensation in nuclear reactors

• Particle-laden flow examples: cyclone separators, air classifiers,dust collectors, and dust-laden environmental flows

• Pneumatic transport examples: transport of cement, grains, andmetal powders

• Fluidized bed examples: fluidized bed reactors, circulating flu-idized beds

• Slurry flow examples: slurry transport, mineral processing

• Hydrotransport examples: mineral processing, biomedical and phys-iochemical fluid systems

• Sedimentation examples: mineral processing



slug flow bubbly, droplet, orparticle-laden flow

stratified/free-surface flow pneumatic transport, hydrotransport, or slurry flow

sedimentation fluidized bed

Figure 18.1.1: Multiphase Flow Regimes


18.3 Approaches to Multiphase Modeling

18.3 Approaches to Multiphase Modeling

Advances in computational fluid mechanics have provided the basis forfurther insight into the dynamics of multiphase flows. Currently thereare two approaches for the numerical calculation of multiphase flows: theEuler-Lagrange approach and the Euler-Euler approach.

18.3.1 The Euler-Lagrange Approach

The Lagrangian discrete phase model in FLUENT (described in Chap-ter 19) follows the Euler-Lagrange approach. The fluid phase is treatedas a continuum by solving the time-averaged Navier-Stokes equations,while the dispersed phase is solved by tracking a large number of parti-cles, bubbles, or droplets through the calculated flow field. The dispersedphase can exchange momentum, mass, and energy with the fluid phase.

A fundamental assumption made in this model is that the dispersed sec-ond phase occupies a low volume fraction, even though high mass loading(mparticles ≥ mfluid) is acceptable. The particle or droplet trajectories arecomputed individually at specified intervals during the fluid phase cal-culation. This makes the model appropriate for the modeling of spraydryers, coal and liquid fuel combustion, and some particle-laden flows,but inappropriate for the modeling of liquid-liquid mixtures, fluidizedbeds, or any application where the volume fraction of the second phaseis not negligible.

18.3.2 The Euler-Euler Approach

In the Euler-Euler approach, the different phases are treated mathemat-ically as interpenetrating continua. Since the volume of a phase cannotbe occupied by the other phases, the concept of phasic volume fractionis introduced. These volume fractions are assumed to be continuousfunctions of space and time and their sum is equal to one. Conserva-tion equations for each phase are derived to obtain a set of equations,which have similar structure for all phases. These equations are closedby providing constitutive relations that are obtained from empirical in-formation, or, in the case of granular flows, by application of kinetictheory.



In FLUENT, three different Euler-Euler multiphase models are available:the volume of fluid (VOF) model, the mixture model, and the Eulerianmodel.

The VOF Model

The VOF model (described in Section 20.2) is a surface-tracking tech-nique applied to a fixed Eulerian mesh. It is designed for two or moreimmiscible fluids where the position of the interface between the fluidsis of interest. In the VOF model, a single set of momentum equations isshared by the fluids, and the volume fraction of each of the fluids in eachcomputational cell is tracked throughout the domain. Applications ofthe VOF model include stratified flows, free-surface flows, filling, slosh-ing, the motion of large bubbles in a liquid, the motion of liquid aftera dam break, the prediction of jet breakup (surface tension), and thesteady or transient tracking of any liquid-gas interface.

The Mixture Model

The mixture model (described in Section 20.3) is designed for two ormore phases (fluid or particulate). As in the Eulerian model, the phasesare treated as interpenetrating continua. The mixture model solves forthe mixture momentum equation and prescribes relative velocities todescribe the dispersed phases. Applications of the mixture model includeparticle-laden flows with low loading, bubbly flows, sedimentation, andcyclone separators. The mixture model can also be used without relativevelocities for the dispersed phases to model homogeneous multiphaseflow.

The Eulerian Model

The Eulerian model (described in Section 20.4) is the most complex ofthe multiphase models in FLUENT. It solves a set of n momentum andcontinuity equations for each phase. Coupling is achieved through thepressure and interphase exchange coefficients. The manner in which thiscoupling is handled depends upon the type of phases involved; granular(fluid-solid) flows are handled differently than non-granular (fluid-fluid)flows. For granular flows, the properties are obtained from application of


18.4 Choosing a Multiphase Model

kinetic theory. Momentum exchange between the phases is also depen-dent upon the type of mixture being modeled. FLUENT’s user-definedfunctions allow you to customize the calculation of the momentum ex-change. Applications of the Eulerian multiphase model include bubblecolumns, risers, particle suspension, and fluidized beds.


The first step in solving any multiphase problem is to determine whichof the regimes described in Section 18.1 best represents your flow. Sec-tion 18.4.1 provides some broad guidelines for determining appropriatemodels for each regime, and Section 18.4.2 provides details about how todetermine the degree of interphase coupling for flows involving bubbles,droplets, or particles, and the appropriate model for different amountsof coupling.

18.4.1 General Guidelines

In general, once you have determined the flow regime that best representsyour multiphase system, you can select the appropriate model based onthe following guidelines. Additional details and guidelines for selectingthe appropriate model for flows involving bubbles, droplets, or particlescan be found in Section 18.4.2.

• For bubbly, droplet, and particle-laden flows in which the dispersed-phase volume fractions are less than or equal to 10%, use the dis-crete phase model. See Chapter 19 for more information about thediscrete phase model.

• For bubbly, droplet, and particle-laden flows in which the phasesmix and/or dispersed-phase volume fractions exceed 10%, use ei-ther the mixture model (described in Section 20.3) or the Eulerianmodel (described in Section 20.4). See Sections 18.4.2 and 20.1 fordetails about how to determine which is more appropriate for yourcase.

• For slug flows, use the VOF model. See Section 20.2 for moreinformation about the VOF model.



• For stratified/free-surface flows, use the VOF model. See Sec-tion 20.2 for more information about the VOF model.

• For pneumatic transport, use the mixture model for homogeneousflow (described in Section 20.3) or the Eulerian model for granularflow (described in Section 20.4). See Sections 18.4.2 and 20.1 fordetails about how to determine which is more appropriate for yourcase.

• For fluidized beds, use the Eulerian model for granular flow. SeeSection 20.4 for more information about the Eulerian model.

• For slurry flows and hydrotransport, use the mixture or Eulerianmodel (described, respectively, in Sections 20.3 and 20.4). SeeSections 18.4.2 and 20.1 for details about how to determine whichis more appropriate for your case.

• For sedimentation, use the Eulerian model. See Section 20.4 formore information about the Eulerian model.

• For general, complex multiphase flows that involve multiple flowregimes, select the aspect of the flow that is of most interest, andchoose the model that is most appropriate for that aspect of theflow. Note that the accuracy of results will not be as good as forflows that involve just one flow regime, since the model you usewill be valid for only part of the flow you are modeling.

18.4.2 Detailed Guidelines

For stratified and slug flows, the choice of the VOF model, as indicatedin Section 18.4.1, is straightforward. Choosing a model for the othertypes of flows is less straightforward. As a general guide, there are someparameters that help to identify the appropriate multiphase model forthese other flows: the particulate loading, β, and the Stokes number, St.(Note that the word “particle” is used in this discussion to refer to aparticle, droplet, or bubble.)



The Effect of Particulate Loading

Particulate loading has a major impact on phase interactions. The par-ticulate loading is defined as the mass density ratio of the dispersed phase(d) to that of the carrier phase (c):

β =αdρd

αcρc(18.4-1)

The material density ratio

γ =ρd

ρc(18.4-2)

is greater than 1000 for gas-solid flows, about 1 for liquid-solid flows,and less than 0.001 for gas-liquid flows.

Using these parameters it is possible to estimate the average distancebetween the individual particles of the particulate phase. An estimateof this distance has been given by Crowe et al. [42]:

L

dd=(π

61 + κ

κ

)1/3

(18.4-3)

where κ = βγ . Information about these parameters is important for

determining how the dispersed phase should be treated. For example,for a gas-particle flow with a particulate loading of 1, the interparticlespace L

ddis about 8; the particle can therefore be treated as isolated (i.e.,

very low particulate loading).

Depending on the particulate loading, the degree of interaction betweenthe phases can be divided into three categories:

• For very low loading, the coupling between the phases is one-way;i.e., the fluid carrier influences the particles via drag and turbu-lence, but the particles have no influence on the fluid carrier. Thediscrete phase, mixture, and Eulerian models can all handle thistype of problem correctly. Since the Eulerian model is the mostexpensive, the discrete phase or mixture model is recommended.



• For intermediate loading, the coupling is two-way; i.e., the fluidcarrier influences the particulate phase via drag and turbulence,but the particles in turn influence the carrier fluid via reductionin mean momentum and turbulence. The discrete phase, mixture,and Eulerian models are all applicable in this case, but you needto take into account other factors in order to decide which modelis more appropriate. See below for information about using theStokes number as a guide.

• For high loading, there is two-way coupling plus particle pressureand viscous stresses due to particles (four-way coupling). Only theEulerian model will handle this type of problem correctly.

The Significance of the Stokes Number

For systems with intermediate particulate loading, estimating the valueof the Stokes number can help you select the most appropriate model.The Stokes number can be defined as the relation between the particleresponse time and the system response time:

St =τdts

(18.4-4)

where τd = ρdd2d

18µcand ts is based on the characteristic length (Ls) and the

characteristic velocity (Vs) of the system under investigation: ts = LsVs

.

For St � 1.0, the particle will follow the flow closely and any of thethree models (discrete phase, mixture, or Eulerian) is applicable; youcan therefore choose the least expensive (the mixture model, in mostcases), or the most appropriate considering other factors. For St > 1.0,the particles will move independently of the flow and either the discretephase model or the Eulerian model is applicable. For St ≈ 1.0, againany of the three models is applicable; you can choose the least expensiveor the most appropriate considering other factors.



Examples

For a coal classifier with a characteristic length of 1 m and a characteristicvelocity of 10 m/s, the Stokes number is 0.04 for particles with a diameterof 30 microns, but 4.0 for particles with a diameter of 300 microns.Clearly the mixture model will not be applicable to the latter case.

For the case of mineral processing, in a system with a characteristiclength of 0.2 m and a characteristic velocity of 2 m/s, the Stokes numberis 0.005 for particles with a diameter of 300 microns. In this case, you canchoose between the mixture and Eulerian models. (The volume fractionsare too high for the discrete phase model, as noted below.)

Other Considerations

Keep in mind that the use of the discrete phase model is limited to lowvolume fractions. Also, the discrete phase model is the only multiphasemodel that allows you to specify the particle distribution or include com-bustion modeling in your simulation.


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